No, they are not. The only way they can connect your wallet to you is if that wallet has on-chain connections to your personally identifiable information, usually through an exchange wallet where you have gone through KYC.
If you don't let those connections happen, no one knows who controls the wallet.
This. But there's also the path of logging your IP address whenever you connect to the Bitcoin / Lightning network. Your ISP does this as a matter of course.
Tor-ify everything.
https://www.torproject.org